Magnetic Transitions of Superconducting Thin Films and Foils. II. Tin

Abstract

The perpendicular and parallel magnetic critical fields of pure tin films and foils have been measured as a function of temperature (${1.3}^{\circ }\mathrm{K}-T_c$) and specimen thickness (500 Å-220 kÅ). The critical field $H_{\perp }$ for specimens of thickness less than a critical thickness $d_c$ is in good agreement with Tinkham's vortex model for thin films if one assumes a thickness dependence for the penetration depth. For thicker films and foils the observed thickness dependence of $H_{\perp }$ is in good agreement with a theory based on the effect of positive surface energy on the free energy of the intermediate state. The measured parallel critical field $H_{\parallel }$ is in excellent agreement with Ginzburg-Landau theory for type-I superconductors in both the thin- and thick-film limits. For films thinner than a critical thickness ${d_c}^{\prime }$, the transition is of second order and the relationship between $H_{\perp }$, $H_{\parallel }$, and the film thickness is in excellent agreement with the "universal curve" of Saint James and de Gennes for second-order transitions. For films thicker than ${d_c}^{\prime }$, the transitions are of first order, and the critical fields approach the Ginzburg-Landau limit valid for $d\gg \lambda$. A comparison of the observed critical thicknesses $d_c$ and ${d_c}^{\prime }$ with theoretical calculations has been made. From the data, bulk values for $\kappa \mathrm{}\left(t\right)\mathrm{}$, $\lambda \mathrm{}\left(t\right)\mathrm{}$, ${\lambda }_L\mathrm{}\left(0\right)\mathrm{}$, ${\xi }_0$, and $\Delta$ have been computed, and the thickness dependence of $\kappa \mathrm{}\left(t\right)\mathrm{}$ and $\lambda \mathrm{}\left(t\right)\mathrm{}$ has been estimated.